Although getting fewer, there are still insurance companies out there who will insure your car under your regular coverage for 'driving school', non-timed events. If you have never tracked your car, instruction is a must......and you can have just as much fun 'un-timed'. I just have my wife use a stop watch every now and again throughout the day. Works plenty good enough for the amount of track time I get.
I don't agree at all that if you can afford to buy it, you should be able to afford to fix it. That's part of what insurance is for....to fix it when it breaks. With no insurance, I would have had none of the 1000 track miles I have to date. If I would have had to buy an expensive one day policy -- probably would have had considerably less, if any, track time.
Steve